Statistical Signal Processing

1. Front Matter

   Pages i-xvii

   PDF

2. Introduction

   • Debasis Kundu, Swagata Nandi

   Pages 1-6

3. Notations and Preliminaries

   • Debasis Kundu, Swagata Nandi

   Pages 7-15

4. Estimation of Frequencies

   • Debasis Kundu, Swagata Nandi

   Pages 17-43

5. Asymptotic Properties

   • Debasis Kundu, Swagata Nandi

   Pages 45-78

6. Estimating the Number of Components

   • Debasis Kundu, Swagata Nandi

   Pages 79-90

7. Real Data Example

   • Debasis Kundu, Swagata Nandi

   Pages 91-99

8. Multidimensional Models

   • Debasis Kundu, Swagata Nandi

   Pages 101-112

9. Related Models

   • Debasis Kundu, Swagata Nandi

   Pages 113-127

10. Back Matter

    Pages 129-132

    PDF

Signal processing may broadly be considered to involve the recovery of information from physical observations. The received signal is usually disturbed by thermal, electrical, atmospheric or intentional interferences. Due to the random nature of the signal, statistical techniques play an important role in analyzing the signal. Statistics is also used in the formulation of the appropriate models to describe the behavior of the system, the development of appropriate techniques for estimation of model parameters and the assessment of the model performances. Statistical signal processing basically refers to the analysis of random signals using appropriate statistical techniques. The main aim of this book is to introduce different signal processing models which have been used in analyzing periodic data, and different statistical and computational issues involved in solving them. We discuss in detail the sinusoidal frequency model which has been used extensively in analyzing periodic data occuring in various fields. We have tried to introduce different associated models and higher dimensional statistical signal processing models which have been further discussed in the literature. Different real data sets have been analyzed to illustrate how different models can be used in practice. Several open problems have been indicated for future research.

• Convergence
• Information Theoretic Criterion
• Least-squares Estimators
• Rate of Convergence
• Sinusoidal Frequency

From the reviews:

 “The book deals with the frequency estimation problem. It is appropriate for senior undergraduate and graduate students specializing in Mathematics or Statistics. … References are listed at the end of each chapter.” (Antonio Napolitano, Mathematical Reviews, January, 2014)

• , Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India

  Debasis Kundu

• , Theoretical Stat and Mathematics Unit, Indian Statistical Institute, New Delhi, India

  Swagata Nandi

Debasis Kundu is currently the Arun Kumar Chair Professor at the Department of Mathematics and Statistics in the Indian Institute of Technology, Kanpur. He received his B-Stat and M-Stat from the Indian Statistical Institute, MA (Mathematics) from the University of Pittsburgh and Ph.D. from the Pennsylvania State University under the guidance of Professor C.R. Rao in the area of statistical signal processing. He has worked in the University of Texas and Dallas for a year before joining the Indian Institute of Technology, Kanpur as an Assistant Professor. His research interests include statistical signal processing, reliability theory, statistical computing, distribution theory and competing risks. He has published more than 175 research papers in different national and international journals. He is a Fellow of the National Academy of Sciences, India and a Fellow of the Royal Statistical Society, UK. He is in the editorial boards of Communications in Statistics - Theory and Methods, Communications in Statistics - Simulation and Computation, Journal of Statistical Theory and Practice, Journal of Statistics and Applications, Journal of Modern Applied Statistical Methods.

Swagata Nandi is currently an Assistant Professor at the Theoretical Statistics and Mathematics Unit of the Indian Statistical Institute, Delhi Center. She received her M.Sc. and Ph.D. from the Indian Institute of Technology. Kanpur. Before joining the Indian Statistical Institute as an Assistant Professor, she was a post doctoral fellow at the University of Heidelberg and at the University of Mannheim. Her research interests include statistical signal processing, analysis of surrogate data, EM algorithm and bootstrapping technique. She has more than 25 research publications in different national and international journals. She is the recipient of the Indian Science Congress Association Young Scientist award and  is the winner of the 'C.L. Chandana Award forStudents'.

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